Hi Angus,
Amalgamated Carburetters Ltd (AMAL) was formed from an amalgamation (!) of the companies making AMAC, Binks and B&B carbies. For 1929 it seems that most of the output was just branded AMAL but there were some remnants of the old order. On the continent, for example, the AMAC brand lived on, and from your lawnmower we see that AMAL were using the Binks brand for some of its industrial output.
I have a little booklet that lists parts for AMAC, Binks and B&B up to 1928 and "AMAL and Binks carburetters" for 1929 and 1930. The Binks carbies shown in the booklet are pretty similar to the AMAL products, but for example the top of the mixing chamber like the one on your mower is shown on the Binks, but not on the AMAL.
In summary, let me guess that AMAL (the company) used the Binks brand for some of its products supplied to industrial customers. You'll probably find that many AMAL parts will suit your Binks.
Cheers
Leon